Mathematics and Statistics Vol. 5(1), pp. 5 - 18
DOI: 10.13189/ms.2017.050102
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Bilinear Multipliers of Weighted Lorentz Spaces and Variable Exponent Lorentz Spaces

Öznur Kulak ^1,*, A. Turan Gürkanlı ^2
1 Department of Banking and Finance, Gorele Applied Sciences Academy, Giresun University, Gorele, Giresun, Turkey
² Department of Mathematics and Computer Sciences, Faculty of Science and Letters, Istanbul Arel University, Tepekent, Istanbul, Turkey

ABSTRACT

Let ω₁, ω₂ be slowly increasing functions and let ω₃ be weight function on ℝⁿ. In section 2 we define a bilinear multiplier from L(p₁, q₁, ω₁dμ) (ℝⁿ) × L(p₂, q₂, ω₂dμ) (ℝⁿ) to L(p₃, q₃, ω₃dμ) (ℝⁿ) by a bounded operator B_m, where 1≤ p₁, p₂, p₃, q₁, q₂, q₃ < ∞ and m (ξ,η) is a bounded, measurable function on ℝⁿ × ℝⁿ. We denote the space of bilinear multipliers of this type by BM (L(p₁, q₁, ω₁dμ) × L(p₂, q₂, ω₂dμ), L(p₃, q₃, ω₃dμ)), and study of the basic properties of this space. We give methods of construction examples of bilinear multipliers. Similarly in section 3, by using variable exponent Lorentz space, we define the bilinear multipliers from L( p₁ (x), q₁ (x)) × L( p₂ (x), q₂ (x)) to L( p₃ (x), q₃ (x)) and discuss basic properties of the space of bilinear multipliers BM (L( p₁ (x), q₁ (x)) × L( p₂ (x), q₂ (x)), L( p₃ (x), q₃ (x))).

KEYWORDS
Bilinear Multipliers, Weighted Lorentz Space, Variable Exponent Lorentz Space

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Öznur Kulak , A. Turan Gürkanlı , "Bilinear Multipliers of Weighted Lorentz Spaces and Variable Exponent Lorentz Spaces," Mathematics and Statistics, Vol. 5, No. 1, pp. 5 - 18, 2017. DOI: 10.13189/ms.2017.050102.

(b). APA Format:
Öznur Kulak , A. Turan Gürkanlı (2017). Bilinear Multipliers of Weighted Lorentz Spaces and Variable Exponent Lorentz Spaces. Mathematics and Statistics, 5(1), 5 - 18. DOI: 10.13189/ms.2017.050102.